Question

gabriels class went on a field trip to the aquarium, where gabriel counted the number of fish in 5 schools that swam by: 70 fish 90 fish 30 fish 82 fish 85 fish what was the mean absolute deviation of the sizes of a school? if the answer is a decimal, round it to the nearest tenth. mean absolute deviation (mad): fish

Explanation:

Step1: Calcular la media

La media $\bar{x}$ de un conjunto de datos $x_1,x_2,\cdots,x_n$ se calcula como $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$. Aquí, $n = 5$, $x_1=70$, $x_2 = 90$, $x_3=30$, $x_4=82$, $x_5=85$.

$\bar{x}=\frac{70 + 90+30+82+85}{5}=\frac{357}{5}=71.4$

Step2: Calcular las desviaciones absolutas

La desviación absoluta de cada dato $x_i$ con respecto a la media $\bar{x}$ es $|x_i-\bar{x}|$.

• Para $x_1 = 70$: $|70 - 71.4|=1.4$
• Para $x_2 = 90$: $|90 - 71.4|=18.6$
• Para $x_3 = 30$: $|30 - 71.4|=41.4$
• Para $x_4 = 82$: $|82 - 71.4|=10.6$
• Para $x_5 = 85$: $|85 - 71.4|=13.6$

Step3: Calcular la media de las desviaciones absolutas (MAD)

La MAD se calcula como $\text{MAD}=\frac{\sum_{i = 1}^{n}|x_i-\bar{x}|}{n}$

$\sum_{i = 1}^{5}|x_i-\bar{x}|=1.4 + 18.6+41.4+10.6+13.6=85.6$

$\text{MAD}=\frac{85.6}{5}=17.12\approx17.1$

Answer:

$17.1$